What is the optimum value for the coefficient of friction of a threaded fastener?

In July 2023, Bill Eccles of Bolt Science presented a paper titled: 'The Goldilocks Zone and the Coefficient of Friction of Threaded Fasteners' at the LUBMAT 2023 conference in the UK. This summarises the paper and adds some background and context.


When a nut is tightened, the bolt is stretched and is resisted by a tensile force within the bolt, the preload. The preload is reacted by a clamp force that pushes the joint plates together.

In most applications, it is the clamp force acting on the joint interface that is the critical parameter. There is no low cost means of measuring or controlling the clamp force so some other, easily measurable quantity is needed. Controlling the torque value applied to the nut being the most popular approach.

Most of the torque that is applied when tightening a nut is used in overcoming friction. The pie chart shows the case for an M12 property class 8.8 bolt being fully tightened with the friction coefficient being 0.12. The torque value is very specific to the coefficient of friction. On the positive front, friction is needed since otherwise the nut would spin off when the socket was removed following tightening.

Increased thread friction causes increased torsional stress.

When a nut is tightened, besides the tensile stress, the bolt is also subjected to torsion. This arises from the thread friction torque and the torque that is needed to stretch the bolt. Accordingly, higher the thread friction, higher will be the torsion in the bolt.

Yielding of the bolt is a consequence of the combined effects of the tensile and torsional stresses. The effect of a high thread friction is to lower the tensile stress present in the bolt at yield. It is from the tensile stress that the preload arises. Consequently, a high friction value reduces the maximum preload that can be achieved.

Although friction can be controlled, to some degree, by the use of wet or dry lubricants, some amount of scatter still occurs. For a given percentage utilisation of the strength of the bolt material, a lower friction value will produce a higher preload. This is due to the reduced torsion being present with a lower friction value.

Hence, just from a purely tightening aspect, a low friction value is desirable since it will allow a higher preload to be achievable and allow this to be doable at a low torque value.

Using the torque-tension equation and understanding that the stretch torque component always acts in the untightening direction, the minimum friction value needed to prevent spontaneous untightening can be derived.

The lowest practical friction value that is currently achievable is of the order of 0.04 which is why such spontaneous loosening is not observed.

It's been known for over 50 years that joint slip can cause self-loosening. (More details) There is a concern that at low values of friction, there is an increased risk of self-loosening. If say, a one-off overload occurred to the assembly that caused joint slip to occur, the fastener would rotate and reduce the preload. With a low friction value, the extent of the preload loss could be such that a more normal loading would be sufficient to cause repeated slip. Such repeated slip can result in a complete loss of the fastener preload.

The Goldilocks Zone for Friction

It is this concern that gives rise to manufacturers limiting the lower friction limit that they will accept for their fasteners. This lower friction limit is well above the friction value required for spontaneous loosening.

This concern about a low friction value gives rise to a Goldilocks zone for fastener friction values. Not too low and not too high, but just right. The range shown above is the VDI 2230 friction coefficient class B.

At the high friction values, there will be a higher torque required to tighten the fastener, a higher torsion in the bolt and a lower preload for a given strength utilisation of the bolt material.

Once a lower acceptable limit is decided upon, the upper limit requires control to limit the preload scatter.

The upper and lower limits of the Goldilocks Zone is subject to judgement. Most volume manufacturers are using fasteners with a coefficient of total friction of around 0.12.

There are obvious advantages to lowering the value. Presently, the 0.04 to 0.08 range is regarded as a no-go zone by most manufacturers producing product in volume. More work is needed to identify the actual true risk of lowering the limit to below 0.08 and under what circumstances or assemblies this would be feasible.

Since the torque value is determined based upon the lowest value of the friction range (as per VDI 2230), changing the lower friction limit would potentially cause the bolts to be over-tightened on existing designs with the attendant risks. So, any significant change to the Goldilocks zone is unlikely to happen any time soon.

To view the conference paper, click here.